# Asymptotic controllability implies feedback stabilization

@article{Clarke1997AsymptoticCI,
title={Asymptotic controllability implies feedback stabilization},
author={Frank H. Clarke and Yu. S. Ledyaev and Eduardo Sontag and Andreĭ I. Subbotin},
journal={IEEE Trans. Autom. Control.},
year={1997},
volume={42},
pages={1394-1407}
}
• Published 1 October 1997
• Mathematics
• IEEE Trans. Autom. Control.
It is shown that every asymptotically controllable system can be globally stabilized by means of some (discontinuous) feedback law. The stabilizing strategy is based on pointwise optimization of a smoothed version of a control-Lyapunov function, iteratively sending trajectories into smaller and smaller neighborhoods of a desired equilibrium. A major technical problem, and one of the contributions of the present paper, concerns the precise meaning of "solution" when using a discontinuous…
546 Citations

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